) Distribution of height of 1000 students is normal with mean 165 cms and standard deviation 15 cms. How many soldiers are of height (i) less than 138 cms (ii) more than 198 cms (iii) between 138 and 198 cms. [P(z=1.8)=0.4641, P(z=2.2)=0.4861]
Answers
Given : Distribution of height of 1000 students is normal with mean 165 cms and standard deviation 15 cms.
[P(z=1.8)=0.4641, P(z=2.2)=0.4861]
To Find : How many soldiers are of height
(i) less than 138 cms
(ii) more than 198 cms
(iii) between 138 and 198 cms.
Solution:
Z score = ( Value - Mean) /SD
Mean = 165
SD = 15
less than 138 cms
=> Z score = ( 138 - 165)/15 = - 1.8 = 0.0359
(0.4641 given is from mid point) 0.0359 is from 0 ( ref attached table)
0.0359 * 1000 = 35.9 = 36
36 soldiers are of height less than 138 cms
more than 198 cms
=> Z score = ( 198 - 165)/15 = 2.2 = 0.9861
(0.48611 given is from mid point) 0.9861 is from 0 ( ref attached table)
0.9861 * 1000 = 986.1 = 986
more than 198 cms = 1000 - 986 = 14
between 138 and 198 cms = 986 - 36 = 950
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